Math Praxis

(0×10^4)+(4×10^3)+(0×10^2)+(5×10^1)+(2×10^0) What number is represented by the base-10 expression shown?

4052

(2x+5x⎯2)−(x+y⎯3y⎯5x+2) Which of the following is equivalent to the preceding expression? A.11x+2y−4 B.3x−2y−4 C.11x−2y D.x−2y

A

1 − 2 5/6 What is the value of the preceding expression? A.−1 5/6 B.−1/6 C.1/6 D.1 5/6

A

A certain polygon has the following attributes. 1.There are 2 pairs of parallel sides. 2.It is a quadrilateral. 3.One pair of parallel sides has length 2, and the other pair of parallel sides has length 4. Which of the following types of polygons has all of the attributes listed? A.Parallelogram B.Rhombus C.Triangle D.Square

A

Carlos makes an annual salary of $65,295. Which of the following is Carlos' salary rounded to the nearest thousand? A.$65,000 B.$65,300 C.$66,000 D.$70,000

A

In a bag there are 28 candies, of which 17 are peppermints and the rest are caramel chews. What is the ratio of the number of caramel chews to the number of peppermints in the bag? A.11 to 17 B.17 to 11 C.17 to 28 D.28 to 17

A

The cost to rent a bus for a field trip is $34.25 per hour, and the duration of the trip is 4 hours and 45 minutes. Which of the following expressions is best for doing a mental calculation to closely estimate the total cost, in dollars, of renting the bus for the trip? Answer the question by selecting the correct response. A.34×5 B.34×4.75 C.34.25×4.75 D.35×5

A

The following figures are the first three figures in a pattern. Three figures are shown. From left to right, the figures are labeled Figure 1, Figure 2, and Figure 3. Each figure consists of connected line segments that make up squares and triangles. Figure 1. Figure 1 consists of eight line segments that make up one square and two triangles. The square is at the center of the figure, and is comprised of four line segments. Two line segments extend outward from the left side of the square to form the first triangle. Two line segments extend outward from the right side of the square to form the second triangle. Figure 2. Figure 2 consists of eleven line segments that make up two squares and two triangles. The squares are positioned side by side at the center of the figure, such that they share one side. Two line segments extend outward from the left side of the square on the left to form the first triangle. Two line segments extend outward from the right side of the square on the right to form the second triangle. Figure 3. Figure 3 consists of fourteen line segments that make up three squares and two triangles. The squares are positioned side by side at the center of the figure, such that each adjacent square shares one side. Two line segments extend outward from the left side of the square on the left to form the first triangle. Two line segments extend outward from the right side of the square on the right to form the second triangle. End figure description. Figure 1 is composed of two triangles and one square. Each figure after figure 1 is composed of two triangles and one square more than the preceding figure. How many line segments are in figure 10 of the pattern? A.35 B.38 C.41 D.44

A

The surface area of a cube is 54 square inches. What is the volume of the cube? A.27 cubic inches B.54 cubic inches C.81 cubic inches D.108 cubic inches

A

Which of the following inequalities is equivalent to the inequality 4x+4≤9x+8? A.x≥−4/5 B.x≤−4/5 C.x≥−12/5 D.x≤−12/5

A

Which of the following is an algebraic expression? A.6x−4 B.6y<4 C.6z=4 D.6+4

A

Which word describes each angle in an equilateral triangle? A.Acute B.Obtuse C.Right D.Straight

A

Which of the following is a statistical question? Select ALL that apply. A.What is the daily high temperature for an August day in Cheyenne, Wyoming? B.How many speeches did George Washington make during his life? C.How many minutes did Hannah spend talking on her phone on August 28, 2016 ? D.What was the average number of miles a week run by the members of the Hereford High School cross-country team last month?

A,D

A unit square is partitioned into identical parts having equal areas. One of the parts is removed from the square, and a shape is formed by the parts that remain after the removal. For which of the following areas of the removed part will the shape that is formed have the greatest area? A.1/4 B.1/5 C.1/6 D.1/7

D

At a flower shop, there are 5 different kinds of flowers: tulips, lilies, daisies, carnations, and roses. There are also 3 different colors of vases to hold the flowers: blue, green, and pink. If one kind of flower and one color of vase to hold them are to be selected at random, what is the probability that the selection will be lilies held in a pink vase? A.2/8 B.2/15 C.1/8 D.1/15

D

2/3÷4/3+3/5×(5/3)^2 Which of the following is equivalent to the preceding expression? A.2/9 B.13/6 C.23/9 D.55/18

B

A window's size is 8 feet by 4 feet. Which of the following units is most appropriate to use to convert the dimensions to metric units? A.Kilometers B.Meters C.Millimeters D.Nanometers

B

If r is a real number, which of the following illustrates the commutative property of multiplication? A.(32)(r)=(3)(2r) B.(32)(r)=(r)(32) C.(32)(r)=(30)(r)+(2)(r) D.(32)(r)=(32)(r)(1)

B

If y=2, what is the value of 4−2(4y)+5y ? A.−22 B.−2 C.22 D.26

B

In the following figure, all small rectangles contained in rectangle EFGH shown have the same area. The figure shows rectangle EFGH. The rectangle contains 50 smaller congruent rectangles arranged in 5 rows of 10 columns. End figure description. How many of the small rectangles must be shaded so that 38 percent of the area of rectangle EFGH is shaded? A.12 B.19 C.31 D.38

B

Lily, Matthew, Natalie, and Owen each walked from their houses to the mall. Lily walked 1/4 mile, Matthew walked 3/8 mile, Natalie walked 5/6 mile, and Owen walked 7/12 mile. Which list shows these distances in order from least to greatest? A.1/4 mile, 3/8 mile, 5/6 mile, 7/12 mile B.1/4 mile, 3/8 mile, 7/12 mile, 5/6 mile C.1/4 mile, 5/6 mile, 3/8 mile, 7/12 mile D.7/12 mile, 3/8 mile, 5/6 mile, 1/4 mile

B

The figure shows a boxplot. The numbers 100 through 1,000, in increments of 100, are indicated on the horizontal axis. The whiskers of the boxplot extend from 200 to 700. A box extends from 300 to 500. A vertical line segment at 400 divides the box into two parts. A point is indicated at 1,000. End figure description. A boxplot for a set of data is shown in the preceding figure. Which of the following is true? A.The only outlier is 200. B.The only outlier is 1,000. C.The only outliers are 200, 700, and 1,000. D.All values greater than 500 or less than 300 are outliers.

B

The figure shows the graph of 4 points labeled J, K, L, and M, in the x y coordinate plane. The number 1 is indicated on both axes. The coordinates of each data point are as follows. Point J. -4,2. Point K. 4,5. Point L. 2,-3. Point M. -3,-3. End figure description. In the preceding coordinate plane, which point is located in Quadrant 1I? A.J B.K C.L D.M

B

The preceding figure is a net for which of the following three-dimensional figures? A.Cube B.Triangular prism C.Rectangular prism D.Triangular pyramid

B

Two friends went out for lunch and decided to share the dessert. One of them ate 1/2 of the dessert, and the other ate 1/3 of the remaining part. What fraction of the dessert was left over? A.1/6 B.1/3 C.2/3 D.5/6

B

What is the least common multiple of 12, 20, and 30 ? A.2 B.60 C.240 D.360

B

Which phrase describes the solution set to the inequality 18b−5<20b+11? A.All numbers that are less than negative 8−8 B.All numbers that are greater than negative 8−8 C.All numbers that are less than 8 D.All numbers that are greater than 8

B

x y 1 1 2 4 3 9 4 16 Which of the following functions could be represented by the preceding table? A.y=2^x B.y=x^2 C.y=2x D.y=5x−4

B

1 tablespoon equals=1/16 cup 1 teaspoon equals=1/3 tablespoon 1 fluid ounce equals=2 tablespoons Each of the preceding conversions shows equivalent measurements. Based on the equivalent measurements, which of the following quantities is greatest? A.12 tablespoons B.7/8 cup C.8 fluid ounces D.45 teaspoons

C

3 less than 4 times the sum of the number x and 15 Which of the following expressions best represents the preceding verbal phrase? A.4x+15−3 B.3−4x+15 C.4(x+15)−3 D.3−4(x+15)

C

A machine that works at a constant rate processes 18 pounds of fruit every 3 hours. At this rate, how many hours does it take the machine to process 72 pounds of fruit? A.4 B.10 C.12 D.15

C

A painter used 1 1/2 cans of paint to paint 2/3 of a room. At this rate, how much more paint does the painter need to paint the remainder of the room? A.1/3 can B.1/2 can C.3/4 can D.1 can

C

At an apple orchard, between 280 and 300 bushels of apples are picked each day during peak harvest season. There are between 42 and 48 pounds of apples in each bushel. Which of the following could be the number of pounds of apples picked at the orchard in one day during peak harvest season? A.9,000 B.11,000 C.13,000 D.15,000

C

In a flower shop, there are 5 roses in every bouquet. The following equation gives the number of roses r used to make b bouquets. r=5b Which of the following sentences best describes the variables r and b in the preceding equation? A.b is a dependent variable, and r is a dependent variable. B.b is a dependent variable, and r is an independent variable. C.b is an independent variable, and r is a dependent variable. D.b is an independent variable, and r is an independent variable.

C

The figure shows four lines labeled q, r, s, and t. Line t is horizontal. Line s is vertical and intersects line t at a right angle. Line r begins below line t and slants upward and to the right. It intersects line t at the point where line s intersects line t. Line q begins below line r and slants upward and to the right at the same slope as line r. It intersects line t to the right of where line s intersects line t. End figure description. In the preceding figure, which two lines form a pair of perpendicular lines? A.Line q and line r B.Line r and line s C.Line s and line t D.Line t and line q

C

The following list shows Caleb's scores for the first 6 quizzes in his algebra class. 90,90,95,90,85,90 If he receives a score of 95 on the 7th quiz, which of the following statements will be true? A.The average (arithmetic mean) of the 7 quiz scores is less than the average of the first 6 quiz scores. B.The mode of the 7 quiz scores is greater than the mode of the first 6 quiz scores. C.The median of the 7 quiz scores is equal to the median of the first 6 quiz scores. D.The range of the 7 quiz scores is greater than the range of the first 6 quiz scores.

C

The following list shows the first six terms of a sequence. 1, 1, 2, 3, 5, 8,... Which of the following formulas can be used to find the terms of the sequence? A.a1=1 an=an−1 for n≥2 B.a1=1 an=an−1+1 for n≥2 C.a1=1 a2=1 an=an−2+an−1 for n≥3 D.a1=1 a2=1 an=an−2+an−1+n−3 for n≥3

C

The following table shows the populations of four neighboring counties. County Population Brookhaven 74,702 Columbus 70,472 Davidson 74,072 Washington 74,720 Quyen lives in the county with a population of 70,000 plus 4,000, plus 70, plus 270,000+4,000+70+2 . In which county does Quyen live? A.Brookhaven B.Columbus C.Davidson D.Washington

C

The formula V equals I times RV=IR relates the voltage V, in volts, to the current I, in amperes, and the resistance R, in ohms, in a circuit. What is the current produced by a 9-volt battery in a circuit with 4 ohms of resistance? A.1.50 amperes B.2.00 amperes C.2.25 amperes D.2.50 amperes

C

Two figures are shown. Figure 1 is a small square. Figure 2 is a large square. End figure description. The preceding figures are squares. Each side in Figure 1 has length 7, and Figure 2 has side lengths that are double those in Figure 1. How do the perimeter and area of Figure 1 compare with the perimeter and area of Figure 2 ? A.The perimeter and area of Figure 2 are double the perimeter and area of Figure 1. B.The perimeter and area of Figure 2 are four times the perimeter and area of Figure 1. C.The perimeter of Figure 2 is double the perimeter of Figure 1, and the area of Figure 2 is four times the area of Figure 1. D.The perimeter of Figure 2 is four times the perimeter of Figure 1, and the area of Figure 2 is eight times the area of Figure 1.

C

a=5,000(1+r) The formula shown can be used to find the amount of money in dollars, a, in an account at the end of one year when $5,000 is invested at simple annual interest rate r for the year. Which of the following represents the independent variable in the formula? A.a B.5,000 C.r D.1+r

C

0.7 is 1/1,000 of what number? A.0.0007 B.0.007 C.70 D.700

D

4x(3x+2y) What does 2y represent in the expression shown? A.A binomial B.A factor C.A coefficient D.A monomial

D

Each of the following four figures uses a number line to represent a different calculation. Figure 1 The figure shows a number line. The numbers negative 10 through 10, in increments of 1, are indicated. Two points are indicated on the number line. The points are indicated at negative 7 and negative 2. An arrow extends from the point at negative 2 to the point at negative 7. End figure description. Figure 2 The figure shows a number line. The numbers negative 10 through 10, in increments of 1, are indicated. Two points are indicated on the number line. The points are indicated at negative 7 and negative 2. An arrow extends from the point at negative 7 to the point at negative 2. End figure description. Figure 3 The figure shows a number line. The numbers negative 10 through 10, in increments of 1, are indicated. Two points are indicated on the number line. The points are indicated at negative 9 and negative 7. An arrow extends from the point at negative 7 to the point at negative 9. End figure description. Figure 4 The figure shows a number line. The numbers negative 10 through 10, in increments of 1, are indicated. Two points are indicated on the number line. The points are indicated at negative 7 and negative 5. An arrow extends from the point at negative 7 to the point at negative 5. End figure description. Which of the preceding figures represents the calculation negative 7 minus negative 2−7−(−2) ? A.Figure 1 B.Figure 2 C.Figure 3 D.Figure 4

D

Mary has a rectangular garden in her backyard. The garden measures 5 3/4 feet wide by 7 1/2 feet long. What is the area of the garden? A.26 1/2 square feet B.35 3/8 square feet C.36 1/8 square feet D.43 1/8 square feet

D

The following boxplots compare the incomes of two professions. The figure shows two boxplots over the same horizontal axis. The horizontal axis is labeled "Annual Income, in thousands of dollars," and the numbers 0 through 140, in increments of 20, are indicated. The boxplots represent the following two professions: Nuclear Engineer and Police Officer. The data represented by the boxplots are as follows. Note that all values are approximate. Nuclear Engineer. The boxplot extends from 50 to 119. A box extends from 60 to 95. A vertical line segment at 70 divides the box into two parts. Police Officer. The boxplot extends from 12 to 60. A box extends from 21 to 44. A vertical line segment at 30 divides the box into two parts. End figure description. Based on the boxplots, which of the following statements is true? A.All nuclear engineers earn more than all police officers. B.Exactly 50% of nuclear engineers earn more than all police officers. C.The range of incomes for nuclear engineers is the same as that for police officers. D.The median income for nuclear engineers is greater than the maximum income for police officers.

D

The following table shows the cost of a membership to Gym G for the five possible membership lengths. Membership Length,in months Cost,in dollars 1 75 3 125 6 200 12 350 24 650 Gym H has the same possible membership lengths, and the cost, y, in dollars, of a membership to Gym H for x months is given by the equation 2y−50x=85. Which of the following is true about the cost, in dollars, of a membership to Gym H compared with the cost of a membership to Gym G? A.The cost of a membership to Gym G is greater than the cost of a membership to Gym H for membership lengths of 6 months or less but is greater for membership lengths of greater than 6 months. B.The cost of a membership to Gym H includes the same initial membership fee as the cost of a membership to Gym G but a greater monthly fee. C.The cost of a membership to Gym H includes a greater initial membership fee than the cost of a membership to Gym G but a lower monthly fee. D.The cost of a membership to Gym G is greater than the cost of a membership to Gym H for any number of months.

D

What is the prime factorization of 3,780 ? A.2×5×6×7×9 B.3×4×5×7×9 C.2×3×6×7×15 D.2×2×3×3×3×5×7

D

What value does the 8 represent in the number 5,836,303 ? A.Eight hundred B.Eight thousand C.Eighty thousand D.Eight hundred thousand

D

Which of the following expressions is equivalent to −4(3−2x) ? A.−2x−12 B.2x−12 C.−8x−12 D.8x−12

D